This calculus 1 derivatives course focuses on differentiating functions. It explains how to find the derivatives of functions that you will typically encounter in your first semester calculus. This course is for university students taking college calculus and high school students who are taking AP Calculus AB.
Here is a list of topics:
1. Derivatives of Constants
2. The Power Rule and Constant Multiple Rule
3. Derivatives of Rational Functions
4. Derivatives of Square Root and Radical Functions
5. How to Differentiate Polynomial Functions Using The Sum and Difference Rule
6. Derivatives of Trigonometric Functions - sin, cos, tan, sec, cot, csc
7. Average Rate of Change vs Instantaneous Rate of Change
8. Writing Equations of the Tangent Line
9. Limit Definition of the Derivative Process
10. Alternative Form of Limit Definition of Derivative
11. Derivatives of Exponential Functions
12. Derivatives of Natural Log Functions - Ln x
13. Differentiation of Logarithmic Functions
14. The Product rule and Quotient Rule
15. The Chain Rule - Plenty of Examples
16. Implicit Differentiation
17. Derivatives of Inverse Trigonometric Functions
18. Logarithmic Differentiation
19. Free Response Video Quiz
This video explains how to find the derivative of a constant which is always zero by the way.
This tutorial explains how to differentiate a monomial using the power rule.
This video discusses the use of the constant multiple rule which is used to differentiate a monomial with a constant in front of it. The power rule is required for this process as well.
This video explains how to find the derivative of a rational function in the form of a fraction using the power rule. You need to rewrite the function before you differentiate it.
This lesson explains how to find the derivative of square root and radical functions by rewriting the function and using the power rule.
This tutorial provides a basic introduction into the derivatives of the six trigonometric functions - sine, cosine, tangent, cotangent, cosecant, and secant.
This video explains how to differentiate polynomial functions using the sum and difference rule.
This tutorial explains how to calculate the average rate of change of a function and the instantaneous rate of change as well. The instantaneous rate of change is equal to the slope of the tangent line which touches the graph at a single point. The average rate of change is equivalent to the slope of the secant line which touches the graph at two points.
This video tutorial explains how to estimate the instantaneous rate of change given a table of values using the average rate of change formula.
This video explains how to write the equation of the tangent line given a function and an x value.
This lecture explains how to find the derivative function using the limit process.
This video provides more examples on limits and derivatives.
This tutorial explains how to calculate the instantaneous rate of change or slope of the tangent line using the alternative form of the limit derivative formula.
This lecture explains how to find the derivative of exponential functions.
This video lesson discusses how to differentiate natural log functions using a simple formula.
This tutorial explains how to find the derivative of logarithmic functions using a simple formula.
This tutorial explains how to find the derivative of two functions multiplied to each other using the product rule.
This tutorial explains how to find the derivative of a division of two functions using the quotient rule.
This lesson provides many examples of finding the derivative of a composite function using the chain rule.
This video explains how to find the derivative of an equation with x and y variables using implicit differentiation.
This video explains how to find the derivative of an inverse trigonometric function such as sin^-1 or arctangent.
This tutorial explains how to differentiate a function with a variable raised to another variable using logarithmic differentiation.
This free response video quiz contains 5 questions with the solutions. It's recommended to pause the video first and work on the problem before viewing the solution.
This video quiz also contains 5 free response questions which covers some of the differentiation techniques covered in this course module.
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